Классификация

Данные и проверка модели

Данные

Wholesale customers Data Set (“Потребители оптовика”)

Данные об оптовых продажах за год в Португалии.

1. FRESH: годовые затраты (у.е.) на свежие продукты (Continuous);
2. MILK: годовые затраты (у.е.) на молочные продукты (Continuous);
3. GROCERY: годовые затраты (у.е.)on grocery products (Continuous);
4. FROZEN: годовые затраты (у.е.) на замороженные продукты (Continuous)
5. DETERGENTS_PAPER: годовые затраты (у.е.) на бытовую химию и бумажную продукцию (Continuous)
6. DELICATESSEN: годовые затраты (у.е.) на деликатесы (Continuous);
7. CHANNEL: канал сбыта - отели/рестораны или розница (Nominal) (1, 2)
8. REGION: регион сбыта - Лиссабон, Порту или другие города (Nominal) (1, 2, 3)

sales.data <- read.csv2("Wholesale.csv", sep = ",")
head(sales.data)

##   Channel Region Fresh Milk Grocery Frozen Detergents_Paper Delicassen
## 1       2      3 12669 9656    7561    214             2674       1338
## 2       2      3  7057 9810    9568   1762             3293       1776
## 3       2      3  6353 8808    7684   2405             3516       7844
## 4       1      3 13265 1196    4221   6404              507       1788
## 5       2      3 22615 5410    7198   3915             1777       5185
## 6       2      3  9413 8259    5126    666             1795       1451

Смешаем признаки, чтобы было интереснее смотреть на значимое число дискриминантных функций.

sales.data$Channel <- as.factor(sales.data$Channel)
sales.data$Region <- as.factor(sales.data$Region)
sales.data$ChannelAndRegion <- with(sales.data, interaction(Channel, Region))

levels(sales.data$Channel)

## [1] "1" "2"

levels(sales.data$Region)

## [1] "1" "2" "3"

levels(sales.data$ChannelAndRegion)

## [1] "1.1" "2.1" "1.2" "2.2" "1.3" "2.3"

Цвета для matrixplot’а.

sales.data <- sales.data[,c("ChannelAndRegion", "Fresh","Milk","Grocery","Frozen","Detergents_Paper","Delicassen")]
factor.colors <- palette(c(rgb(134,82,187, maxColorValue=255),
    rgb(148,195,92, maxColorValue=255),
    rgb(189,85,126, maxColorValue=255),
    rgb(146,180,183, maxColorValue=255),
    rgb(196,112,62, maxColorValue=255),
    rgb(75,64,63, maxColorValue=255)))

Колчичество индивидов по группам.

sapply(levels(sales.data$ChannelAndRegion), function(level){
  nrow(sales.data[sales.data$ChannelAndRegion == level,])
})

## 1.1 2.1 1.2 2.2 1.3 2.3 
##  59  18  28  19 211 105

Matrixplot.

pairs.panels(sales.data[,c("Fresh","Milk","Grocery","Frozen","Detergents_Paper","Delicassen")],
               bg=factor.colors[sales.data$ChannelAndRegion],
               pch=21,
               lm=TRUE, 
               lwd = 1,
               ellipses = FALSE)

Прологорифмируем все.

sales.data.log <- sales.data
sales.data.log$Fresh <- log(sales.data.log$Fresh)
sales.data.log$Milk <- log(sales.data.log$Milk)
sales.data.log$Grocery <- log(sales.data.log$Grocery)
sales.data.log$Frozen <- log(sales.data.log$Frozen)
sales.data.log$Detergents_Paper <- log(sales.data.log$Detergents_Paper)
sales.data.log$Delicassen <- log(sales.data.log$Delicassen)

Снова посмотрим на matrixplot.

nums <- c("Fresh","Milk","Grocery","Frozen","Detergents_Paper","Delicassen")
pairs.panels(sales.data.log[,nums],
               bg=factor.colors[sales.data.log$ChannelAndRegion],
               pch=21,
               lm=TRUE, 
               lwd = 1,
               ellipses = FALSE)

Уберем аутлайер, который видно в строке с Grocery.

row <- which.min(sales.data.log[,"Grocery"])
sales.data.log <- sales.data.log[-row,]

Проверка модели

Проверим нормальность.

mshapiro.test(t(as.matrix(sales.data.log[,nums])))

## 
##  Shapiro-Wilk normality test
## 
## data:  Z
## W = 0.88598, p-value < 2.2e-16

Гипотеза о номальости отвергается.

Проверим равенство ковариационных матриц.

boxM(sales.data.log[,nums], sales.data.log$ChannelAndRegion)

## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  sales.data.log[, nums]
## Chi-Sq (approx.) = 319.99, df = 105, p-value < 2.2e-16

Гипотеза о равенсвте ковариационных матриц отвергается.

Значимость различия групп

Wilks’ Lambda Test:

sales.manova <- manova(cbind(Fresh,Milk,Grocery,Frozen,Detergents_Paper,Delicassen) ~ ChannelAndRegion , data = sales.data.log)
summary(sales.manova, test = "Wilks")

##                   Df   Wilks approx F num Df den Df    Pr(>F)    
## ChannelAndRegion   5 0.39363   14.997     30   1714 < 2.2e-16 ***
## Residuals        433                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Гипотеза о равенстве средних по группам отвергается, разница между группами есть. (Все это верно в нормальной модели, которой здесь нет.)

Pooled Covarience Matrix

cov.list <- lapply(levels(sales.data.log$ChannelAndRegion), function(group){
 (nrow(sales.data.log[sales.data.log$ChannelAndRegion == group,nums]) - 1) * cov(sales.data.log[sales.data.log$ChannelAndRegion == group,nums])
})
cov.pooled <- Reduce("+",cov.list)/(nrow(sales.data.log) - length(levels(sales.data.log$ChannelAndRegion)))

Расстояние Махаланобиса между группами (Hotelling T2 test).

mach <- pairwise.mahalanobis(sales.data.log[,nums], grouping = sales.data.log$ChannelAndRegion, cov = cov.pooled)
print(mach)

## $means
##            1        2        3        4        5        6
## 1.1 9.001382 7.756570 7.961288 7.573781 6.057642 6.556345
## 2.1 7.902661 9.124783 9.656924 7.271975 8.726458 7.194342
## 1.2 8.700916 7.431286 8.190612 7.819395 5.784568 6.652988
## 2.2 8.305092 8.837793 9.457913 6.864545 8.665397 6.638330
## 1.3 8.896088 7.709915 7.922872 7.458495 5.931266 6.528948
## 2.3 8.462722 9.040616 9.491755 6.769726 8.553101 6.913929
## 
## $cov
##                        Fresh      Milk      Grocery       Frozen
## Fresh             2.14050968 0.1235884 -0.014162411  0.671802816
## Milk              0.12358843 0.7825135  0.454890227  0.126308889
## Grocery          -0.01416241 0.4548902  0.598416920  0.001437061
## Frozen            0.67180282 0.1263089  0.001437061  1.553779056
## Detergents_Paper -0.07665753 0.4795283  0.543787961 -0.067978106
## Delicassen        0.55015096 0.3762369  0.222884279  0.481325520
##                  Detergents_Paper Delicassen
## Fresh                 -0.07665753  0.5501510
## Milk                   0.47952833  0.3762369
## Grocery                0.54378796  0.2228843
## Frozen                -0.06797811  0.4813255
## Detergents_Paper       1.36805416  0.1690879
## Delicassen             0.16908785  1.7046792
## 
## $distance
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
## [1,] 0.0000000 6.7703842 1.0105616 5.8524515 0.0244341 5.6786027
## [2,] 6.7703842 0.0000000 7.4268749 0.5362603 7.1439997 0.5766334
## [3,] 1.0105616 7.4268749 0.0000000 6.9662658 0.9662989 7.0933574
## [4,] 5.8524515 0.5362603 6.9662658 0.0000000 6.2212546 0.1630954
## [5,] 0.0244341 7.1439997 0.9662989 6.2212546 0.0000000 6.0067245
## [6,] 5.6786027 0.5766334 7.0933574 0.1630954 6.0067245 0.0000000

P-values (F distr.):

num.of.groups <- length(levels(sales.data.log$ChannelAndRegion))
p.vals <- matrix(0, nrow = num.of.groups, ncol = num.of.groups)
rownames(p.vals) <- levels(sales.data.log$ChannelAndRegion)
colnames(p.vals) <- levels(sales.data.log$ChannelAndRegion)

for(i in 1:num.of.groups){
  for(j in i:num.of.groups){
    n1 <- nrow(sales.data.log[sales.data.log$ChannelAndRegion == levels(sales.data.log$ChannelAndRegion)[i],])
    n2 <- nrow(sales.data.log[sales.data.log$ChannelAndRegion == levels(sales.data.log$ChannelAndRegion)[j],])
    m <-  n1 + n2 
    p <- length(nums)
    scaler <- 1/(1/n1 + 1/n2)  * (m - p + 1)/(m*p)
    p.vals[i,j] <-  1 - pf(scaler * mach$distance[i,j], p, m - p + 1)
    p.vals[j,i] <- p.vals[i,j]
  }
}

print(p.vals, digits = 3)

##          1.1      2.1      1.2      2.2      1.3   2.3
## 1.1 1.00e+00 8.45e-11 1.03e-02 5.17e-10 9.81e-01 0.000
## 2.1 8.45e-11 1.00e+00 8.91e-08 6.41e-01 0.00e+00 0.214
## 1.2 1.03e-02 8.91e-08 1.00e+00 1.09e-07 9.98e-04 0.000
## 2.2 5.17e-10 6.41e-01 1.09e-07 1.00e+00 1.11e-16 0.865
## 1.3 9.81e-01 0.00e+00 9.98e-04 1.11e-16 1.00e+00 0.000
## 2.3 0.00e+00 2.14e-01 0.00e+00 8.65e-01 0.00e+00 1.000

Гипотеза о попарном равенстве средних, для групп 2.1, 2.2, 2.3 не отвергается. То же самое можно сказать про группы 1.1 и 1.3. Остальные p-value меньше 0.05.

Классификация

LDA

sales.lda <- lda(sales.data.log[,nums], sales.data.log$ChannelAndRegion)
sales.lda

## Call:
## lda(sales.data.log[, nums], sales.data.log$ChannelAndRegion)
## 
## Prior probabilities of groups:
##        1.1        2.1        1.2        2.2        1.3        2.3 
## 0.13439636 0.04100228 0.06378132 0.04328018 0.47835991 0.23917995 
## 
## Group means:
##        Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## 1.1 9.001382 7.756570 7.961288 7.573781         6.057642   6.556345
## 2.1 7.902661 9.124783 9.656924 7.271975         8.726458   7.194342
## 1.2 8.700916 7.431286 8.190612 7.819395         5.784568   6.652988
## 2.2 8.305092 8.837793 9.457913 6.864545         8.665397   6.638330
## 1.3 8.896088 7.709915 7.922872 7.458495         5.931266   6.528948
## 2.3 8.462722 9.040616 9.491755 6.769726         8.553101   6.913929
## 
## Coefficients of linear discriminants:
##                            LD1        LD2        LD3         LD4
## Fresh            -0.0396896934  0.2734213 -0.5263659 -0.04083656
## Milk              0.1117766413  1.0862091  0.6899832  0.53074717
## Grocery           0.4657727887 -1.4867393 -0.9360518  0.48138177
## Frozen           -0.1422786729 -0.4292839  0.5045370 -0.35985035
## Detergents_Paper  0.5546018618  0.2902393  0.1930161 -0.70847849
## Delicassen        0.0003849479 -0.1363020  0.2111597  0.43925071
##                         LD5
## Fresh            0.46060960
## Milk             0.09703529
## Grocery          0.09739006
## Frozen           0.36298710
## Detergents_Paper 0.06914301
## Delicassen       0.05847696
## 
## Proportion of trace:
##    LD1    LD2    LD3    LD4    LD5 
## 0.9409 0.0455 0.0088 0.0038 0.0010

Plug-in classification table

sales.lda.predict <- predict(sales.lda, sales.data.log[,nums])$class
table(sales.lda.predict, sales.data.log$ChannelAndRegion) #Качество классификации

##                  
## sales.lda.predict 1.1 2.1 1.2 2.2 1.3 2.3
##               1.1   0   0   0   0   0   0
##               2.1   0   1   0   0   0   0
##               1.2   1   0   2   0   2   0
##               2.2   0   0   0   0   0   0
##               1.3  53   2  25   2 190   8
##               2.3   5  15   1  17  18  97

Cross-validation table

sales.lda <- lda(sales.data.log[,nums], sales.data.log$ChannelAndRegion, CV = TRUE)
table(sales.lda$class, sales.data.log$ChannelAndRegion) #cross-validation 

##      
##       1.1 2.1 1.2 2.2 1.3 2.3
##   1.1   0   0   0   0   0   0
##   2.1   0   0   0   0   0   0
##   1.2   1   0   1   0   2   0
##   2.2   0   0   0   0   0   0
##   1.3  53   2  26   2 189   8
##   2.3   5  16   1  17  19  97

Out-of-sample

sales.train <- sales.data.log[seq(1,nrow(sales.data.log),2),]
sales.unknown <- sales.data.log[-seq(1,nrow(sales.data.log),2),]

sales.lda <- lda(sales.train[,nums], sales.train$ChannelAndRegion)
sales.lda

## Call:
## lda(sales.train[, nums], sales.train$ChannelAndRegion)
## 
## Prior probabilities of groups:
##        1.1        2.1        1.2        2.2        1.3        2.3 
## 0.13181818 0.04090909 0.05454545 0.05454545 0.45454545 0.26363636 
## 
## Group means:
##        Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## 1.1 8.930045 7.831360 7.988323 7.547163         6.291285   6.367474
## 2.1 8.195412 9.176180 9.666030 7.573735         8.949307   7.155830
## 1.2 8.606798 7.474090 8.402664 7.867956         6.040711   6.620134
## 2.2 8.337416 9.061595 9.556045 6.710669         8.811622   6.418384
## 1.3 8.946080 7.772489 7.869457 7.633361         5.855567   6.614237
## 2.3 8.504103 9.027258 9.524591 6.631687         8.548342   6.916502
## 
## Coefficients of linear discriminants:
##                           LD1        LD2        LD3          LD4
## Fresh             0.022882343  0.2383549 -0.2874884 -0.241828840
## Milk              0.210242390  1.2421383  0.1757561  0.429071703
## Grocery           0.306202601 -1.8390170 -0.7365692 -0.136321921
## Frozen           -0.262471915 -0.3458249  0.7223686 -0.001420295
## Detergents_Paper  0.617210223  0.4489793  0.5532875 -0.236530504
## Delicassen        0.002034182 -0.1351499 -0.1024414  0.660915243
##                          LD5
## Fresh             0.29574320
## Milk             -0.86162878
## Grocery          -0.45044941
## Frozen           -0.08988061
## Detergents_Paper  0.66048779
## Delicassen        0.41398995
## 
## Proportion of trace:
##    LD1    LD2    LD3    LD4    LD5 
## 0.9100 0.0631 0.0178 0.0082 0.0009

Plug-in classification table

sales.lda.predict <- predict(sales.lda, sales.unknown[,nums])$class
table(sales.lda.predict, sales.unknown$ChannelAndRegion) #Качество классификации

##                  
## sales.lda.predict 1.1 2.1 1.2 2.2 1.3 2.3
##               1.1   1   0   0   0   0   0
##               2.1   0   1   0   0   0   0
##               1.2   1   0   1   0   5   0
##               2.2   0   0   0   0   0   0
##               1.3  26   1  15   1  91   3
##               2.3   2   7   0   6  14  44

partimat(ChannelAndRegion ~ ., sales.data.log[,c(nums, "ChannelAndRegion")], method="lda")

QDA

sales.qda <- qda(sales.data.log[,nums], sales.data.log$ChannelAndRegion)
sales.qda

## Call:
## qda(sales.data.log[, nums], sales.data.log$ChannelAndRegion)
## 
## Prior probabilities of groups:
##        1.1        2.1        1.2        2.2        1.3        2.3 
## 0.13439636 0.04100228 0.06378132 0.04328018 0.47835991 0.23917995 
## 
## Group means:
##        Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## 1.1 9.001382 7.756570 7.961288 7.573781         6.057642   6.556345
## 2.1 7.902661 9.124783 9.656924 7.271975         8.726458   7.194342
## 1.2 8.700916 7.431286 8.190612 7.819395         5.784568   6.652988
## 2.2 8.305092 8.837793 9.457913 6.864545         8.665397   6.638330
## 1.3 8.896088 7.709915 7.922872 7.458495         5.931266   6.528948
## 2.3 8.462722 9.040616 9.491755 6.769726         8.553101   6.913929

Plug-in classification table

sales.qda.predict <- predict(sales.qda, sales.data.log[,nums])$class
table(sales.qda.predict, sales.data.log$ChannelAndRegion) #Качество классификации

##                  
## sales.qda.predict 1.1 2.1 1.2 2.2 1.3 2.3
##               1.1   2   0   0   0   3   0
##               2.1   0   2   0   0   0   3
##               1.2   1   0   4   0   1   0
##               2.2   0   0   0   5   0   0
##               1.3  50   3  24   1 183   6
##               2.3   6  13   0  13  23  96

Cross-validation table

sales.qda <- qda(sales.data.log[,nums], sales.data.log$ChannelAndRegion, CV = TRUE)
table(sales.qda$class, sales.data.log$ChannelAndRegion) #cross-validation 

##      
##       1.1 2.1 1.2 2.2 1.3 2.3
##   1.1   0   0   0   0   4   0
##   2.1   0   1   0   0   0   4
##   1.2   1   0   2   0   2   0
##   2.2   0   0   0   2   0   2
##   1.3  52   3  26   2 181  11
##   2.3   6  14   0  15  23  88

Out-of-sample

sales.qda <- qda(sales.train[,nums], sales.train$ChannelAndRegion)
sales.qda

## Call:
## qda(sales.train[, nums], sales.train$ChannelAndRegion)
## 
## Prior probabilities of groups:
##        1.1        2.1        1.2        2.2        1.3        2.3 
## 0.13181818 0.04090909 0.05454545 0.05454545 0.45454545 0.26363636 
## 
## Group means:
##        Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## 1.1 8.930045 7.831360 7.988323 7.547163         6.291285   6.367474
## 2.1 8.195412 9.176180 9.666030 7.573735         8.949307   7.155830
## 1.2 8.606798 7.474090 8.402664 7.867956         6.040711   6.620134
## 2.2 8.337416 9.061595 9.556045 6.710669         8.811622   6.418384
## 1.3 8.946080 7.772489 7.869457 7.633361         5.855567   6.614237
## 2.3 8.504103 9.027258 9.524591 6.631687         8.548342   6.916502

Plug-in classification table

sales.qda.predict <- predict(sales.qda, sales.unknown[,nums])$class
table(sales.qda.predict, sales.unknown$ChannelAndRegion) #Качество классификации

##                  
## sales.qda.predict 1.1 2.1 1.2 2.2 1.3 2.3
##               1.1   1   0   0   0   3   0
##               2.1   0   2   0   1   0   3
##               1.2   2   0   1   0   0   1
##               2.2   1   0   0   0   1   5
##               1.3  24   1  15   1  92   4
##               2.3   2   6   0   5  14  34

partimat(ChannelAndRegion ~ ., sales.data.log[,c(nums, "ChannelAndRegion")], method="qda")

Объединение групп

sales.data.log$ChannelAndRegion <- mapvalues(sales.data.log$ChannelAndRegion, from = c("2.1", "2.2", "2.3"), to = c("Shops", "Shops", "Shops"))
sales.data.log$ChannelAndRegion <- mapvalues(sales.data.log$ChannelAndRegion, from = c("1.1", "1.3"), to = c("HotelsLR", "HotelsLR"))
sales.data.log$ChannelAndRegion <- mapvalues(sales.data.log$ChannelAndRegion, from = "1.2", to = "HotelsP")

sapply(levels(sales.data.log$ChannelAndRegion), function(level){
  nrow(sales.data.log[sales.data.log$ChannelAndRegion == level,])
})

## HotelsLR    Shops  HotelsP 
##      269      142       28

Классификация

LDA

sales.lda <- lda(sales.data.log[,nums], sales.data.log$ChannelAndRegion)
sales.lda

## Call:
## lda(sales.data.log[, nums], sales.data.log$ChannelAndRegion)
## 
## Prior probabilities of groups:
##   HotelsLR      Shops    HotelsP 
## 0.61275626 0.32346241 0.06378132 
## 
## Group means:
##             Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## HotelsLR 8.919183 7.720148 7.931298 7.483780         5.958984   6.534957
## Shops    8.370637 9.024146 9.508164 6.846079         8.590101   6.912599
## HotelsP  8.700916 7.431286 8.190612 7.819395         5.784568   6.652988
## 
## Coefficients of linear discriminants:
##                            LD1        LD2
## Fresh            -0.0367761814 -0.1703317
## Milk              0.1138712993 -1.1694579
## Grocery           0.4658743718  1.6489755
## Frozen           -0.1478409895  0.3239726
## Detergents_Paper  0.5554846945 -0.3446850
## Delicassen       -0.0007181123  0.1139285
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9595 0.0405

Plug-in classification table

sales.lda.predict <- predict(sales.lda, sales.data.log[,nums])$class
table(sales.lda.predict, sales.data.log$ChannelAndRegion) #Качество классификации

##                  
## sales.lda.predict HotelsLR Shops HotelsP
##          HotelsLR      243    12      26
##          Shops          23   130       1
##          HotelsP         3     0       1

Cross-validation table

sales.lda <- lda(sales.data.log[,nums], sales.data.log$ChannelAndRegion, CV = TRUE)
table(sales.lda$class, sales.data.log$ChannelAndRegion) #cross-validation 

##           
##            HotelsLR Shops HotelsP
##   HotelsLR      242    12      26
##   Shops          24   130       1
##   HotelsP         3     0       1

Out-of-sample

sales.train <- sales.data.log[seq(1,nrow(sales.data.log),2),]
sales.unknown <- sales.data.log[-seq(1,nrow(sales.data.log),2),]

sales.lda <- lda(sales.train[,nums], sales.train$ChannelAndRegion)
sales.lda

## Call:
## lda(sales.train[, nums], sales.train$ChannelAndRegion)
## 
## Prior probabilities of groups:
##   HotelsLR      Shops    HotelsP 
## 0.58636364 0.35909091 0.05454545 
## 
## Group means:
##             Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## HotelsLR 8.942476 7.785723 7.896179 7.613983         5.953519   6.558763
## Shops    8.443616 9.049440 9.545482 6.751006         8.634013   6.868104
## HotelsP  8.606798 7.474090 8.402664 7.867956         6.040711   6.620134
## 
## Coefficients of linear discriminants:
##                          LD1         LD2
## Fresh             0.01961188 -0.19667436
## Milk              0.20985568 -1.28921833
## Grocery           0.32767711  1.90387744
## Frozen           -0.26903331  0.28970854
## Detergents_Paper  0.60093136 -0.47452935
## Delicassen        0.01450623  0.09234381
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9369 0.0631

Plug-in classification table

sales.lda.predict <- predict(sales.lda, sales.unknown[,nums])$class
table(sales.lda.predict, sales.unknown$ChannelAndRegion) #Качество классификации

##                  
## sales.lda.predict HotelsLR Shops HotelsP
##          HotelsLR      121     5      15
##          Shops          13    58       0
##          HotelsP         6     0       1

partimat(ChannelAndRegion ~ ., sales.data.log[,c(nums, "ChannelAndRegion")], method="lda")

QDA

sales.qda <- qda(sales.data.log[,nums], sales.data.log$ChannelAndRegion)
sales.qda

## Call:
## qda(sales.data.log[, nums], sales.data.log$ChannelAndRegion)
## 
## Prior probabilities of groups:
##   HotelsLR      Shops    HotelsP 
## 0.61275626 0.32346241 0.06378132 
## 
## Group means:
##             Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## HotelsLR 8.919183 7.720148 7.931298 7.483780         5.958984   6.534957
## Shops    8.370637 9.024146 9.508164 6.846079         8.590101   6.912599
## HotelsP  8.700916 7.431286 8.190612 7.819395         5.784568   6.652988

Plug-in classification table

sales.qda.predict <- predict(sales.qda, sales.data.log[,nums])$class
table(sales.qda.predict, sales.data.log$ChannelAndRegion) #Качество классификации

##                  
## sales.qda.predict HotelsLR Shops HotelsP
##          HotelsLR      237    10      26
##          Shops          29   132       0
##          HotelsP         3     0       2

Cross-validation table

sales.qda <- qda(sales.data.log[,nums], sales.data.log$ChannelAndRegion, CV = TRUE)
table(sales.qda$class, sales.data.log$ChannelAndRegion) #cross-validation 

##           
##            HotelsLR Shops HotelsP
##   HotelsLR      237    13      27
##   Shops          29   129       0
##   HotelsP         3     0       1

Out-of-sample

sales.qda <- qda(sales.train[,nums], sales.train$ChannelAndRegion)
sales.qda

## Call:
## qda(sales.train[, nums], sales.train$ChannelAndRegion)
## 
## Prior probabilities of groups:
##   HotelsLR      Shops    HotelsP 
## 0.58636364 0.35909091 0.05454545 
## 
## Group means:
##             Fresh     Milk  Grocery   Frozen Detergents_Paper Delicassen
## HotelsLR 8.942476 7.785723 7.896179 7.613983         5.953519   6.558763
## Shops    8.443616 9.049440 9.545482 6.751006         8.634013   6.868104
## HotelsP  8.606798 7.474090 8.402664 7.867956         6.040711   6.620134

Plug-in classification table

sales.qda.predict <- predict(sales.qda, sales.unknown[,nums])$class
table(sales.qda.predict, sales.unknown$ChannelAndRegion) #Качество классификации

##                  
## sales.qda.predict HotelsLR Shops HotelsP
##          HotelsLR      122     6      15
##          Shops          17    56       0
##          HotelsP         1     1       1

partimat(ChannelAndRegion ~ ., sales.data.log[,c(nums, "ChannelAndRegion")], method="qda")